Integrable hydrodynamics of Calogero–Sutherland model: bidirectional Benjamin–Ono equation
Integrable hydrodynamics of Calogero–Sutherland model: bidirectional Benjamin–Ono equation
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DOI：
10.1088/1751-8113/42/13/135201
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发表时间：
2008-10
期刊：
影响因子：
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通讯作者：
A. Abanov;E. Bettelheim;P. Wiegmann
中科院分区：
文献类型：
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作者：
A. Abanov;E. Bettelheim;P. Wiegmann
我们开发了经典卡洛杰罗-萨瑟兰液体的流体动力学描述：具有无限数量粒子和非零粒子密度的卡洛杰罗-萨瑟兰模型。为液体的密度场和速度场编写的流体动力学方程被证明是本杰明-小野方程的双向模拟。众所周知，后者描述了深层分层流体的内波。我们证明了双向本杰明-小野方程似乎是修改后的 KP 层次结构的真实约简。我们推导了手性非线性方程，它表现为双向方程的手性约简。传统的本杰明-小野方程是大密度下手性非线性方程的简并。我们构造了双向本杰明-小野方程和手性非线性方程的多相解。
We develop a hydrodynamic description of the classical Calogero–Sutherland liquid: a Calogero–Sutherland model with an infinite number of particles and a non-vanishing density of particles. The hydrodynamic equations, being written for the density and velocity fields of the liquid, are shown to be a bidirectional analog of the Benjamin–Ono equation. The latter is known to describe internal waves of deep stratified fluids. We show that the bidirectional Benjamin–Ono equation appears as a real reduction of the modified KP hierarchy. We derive the chiral nonlinear equation which appears as a chiral reduction of the bidirectional equation. The conventional Benjamin–Ono equation is a degeneration of the chiral nonlinear equation at large density. We construct multi-phase solutions of the bidirectional Benjamin–Ono equations and of the chiral nonlinear equations.